Consider an experiment that consists of counting the number of a particles given off in aone-second interval by one gram of radioactive material. If we know from past experiencethat, on the average, 3 such a-particles are given off, what is a good approximation to theprobability that at least 2 a-particles will appear?

Answered: Consider an experiment that consists of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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. Given a normal random variable X with mean μ = 100 and variance o² = 49 if we randomly observe X=30, is this an unusual observation? (a) This would be an unusual observation because it lies less than 3 standard deviations away from the mean. (b) This would not be an unusual observation because it lies less than 3 standard deviations away from the mean. (c) This would be an unusual observation because it lies more than 3 standard deviations away from the mean. (d) This would not be an unusual observation because it lies more than 3 standard deviations away from the mean.
You are conducting a study to see if the average male life expectancy is significantly different from 82. If your null and alternative hypothesis are:H0:μ=82H1:μ≠82Then the test is: two tailed left tailed right tailed
If all the possible random samples with n = 36 scores are selected from a normal population with µ = 80 and σ = 18, and the mean is calculated for each sample, then what is the average of all the sample means? a. 80 b. 6 c. 2 d. It cannot be determined without additional information.
Given an experiment with H0:μ=35,Ha:μ<35H0:μ=35,Ha:μ<35, and a possible correct value of 32, you obtain a sample statistic of x¯=33x¯=33. After doing analysis, you realize that the sample size n is actually larger than you first thought. Which of the following results from reworking with the increase in sample size? a.Decrease in probability of a Type I error; increase in probability of a Type II error; increase in power b.Decrease in probability of a Type I error; decrease in probability of a Type II error; increase in power c.Increase in probability of a Type I error; increase in probability of a Type II error; decrease in power. d.Increase in probability of a Type I error; decrease in probability of a Type II error; decrease in power. e.Decrease in probability of a Type I error; decrease in probability of a Type II error; decrease in power.
1.The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 8880 observations, the sample mean interval was x1 = 63.0 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 25,691 observations, the sample mean time interval was x2 = 70.2 minutes. Historical data suggest that ?1 = 8.70 minutes and ?2 = 12.48 minutes. Let ?1 be the population mean of x1 and let ?2 be the population mean of x2. (a) Compute a 95% confidence interval for ?1 – ?2. (Use 2 decimal places.) lower limit upper limit (b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and…
Suppose that in constructing a single-family house, the time X (in days) necessary for laying the foundation has a Beta distribution with A = 2, B = 5, alpha = 2, beta = 3. What is the expected number of days to finish the foundation? 1.2 O 2.4 3.2 4.7 5.5 Question 32 Suppose that in constructing a single-family house, the time X (in days) necessary for laying the foundation has a Beta distribution with A = 2, B = 5, alpha = 2, beta = 3. What is the probability that it takes at most 3 days? 21% 31% 41% 51%
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4. The probability that the injection of a Covid-19 vaccine will create an unexpected reaction for a human is 0.001. Out of 2000 people, calculate the probability of people will suffer an unexpected reaction (a) exactly 3, (b) more than 2.
A simple random sample of size 144 is selected from a population with p = 0.5. 4a. What is the expected value of p̅?
Suppose we are developing a new drug that is supposed to improve the recovery time of an illness. We want to investigate if this is true. We conduct an experiment: we randomize twenty participants into two groups of size n = 10 each. In one group, we give the participants the drug. In the other group, we give them a placebo. We measure the recovery time of the participants in days. We observe the following data: • In the group given the drug, we observe recovery times (yı,..., Y10) = (15, 10, 13, 7,9, 8, 21,9, 14, 8), with ĝ1 = 11.4. • In the group given the placebo, we observe recovery times (yı1,..., Y20) = (15, 14, 12, 8, 14, 7, 16, 10, 15, 12) with j2 = 12.3. Assume that the data in each group follow Normal(µ1,0²) and Normal(42, o²) distributions respec- tively for the drug and placebo groups, o2 15. We want to test the following hypothesis: Ho : µ1 – 12 = 0 versus HA: µ1 – 42 < 0, using the test statistic T(Y) = Y1 – Ý2. a) Define the rejection region as {y : ĝı – 2 < c1} where ci…
Given that we have a mass "x" (in grams) of a certain object and it will be estimated using the average of several measurements. Suppose the measurements are treated independently and identically distributed random variables, each with mean "x" and variance 3. How many measurements need to be made so at least 95% sure that the estimate is within 0.7 grams of the real value? Note: Must be a whole number.

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